Entropy Change of the Universe when Water is brought into contact with a High Temperature Thermal Reservoir

Entropy Change of the Universe:
The entropy change of the universe can be determined by considering the entropy change of the system (water) and the surroundings (thermal reservoir). According to the second law of thermodynamics, the total entropy change of the universe is always positive or zero, but it cannot be negative.

Entropy Change of the Reservoir:
When the water at room temperature comes into contact with the high-temperature thermal reservoir, heat flows from the reservoir to the water until they reach thermal equilibrium. As a result, the entropy change of the thermal reservoir is given by:

ΔS_reservoir = Q_reservoir / T_reservoir

where ΔS_reservoir is the entropy change of the reservoir, Q_reservoir is the heat transferred from the reservoir, and T_reservoir is the temperature of the reservoir.

Entropy Change of the Water:
The entropy change of the water can be calculated using the equation:

ΔS_water = Q_water / T_water

where ΔS_water is the entropy change of the water, Q_water is the heat transferred to the water, and T_water is the temperature of the water.

Entropy Change of the Universe:
Since the water and the reservoir are in thermal contact and heat is transferred between them, the entropy change of the universe can be obtained by summing up the entropy changes of the reservoir and the water:

ΔS_universe = ΔS_reservoir + ΔS_water

Explanation of the Correct Answer:
In this scenario, the water at room temperature is brought into contact with a high-temperature thermal reservoir. As a result, heat flows from the reservoir to the water until they reach thermal equilibrium. Since the thermal reservoir is at a higher temperature than the water, the heat transfer occurs from the reservoir to the water.

The entropy change of the reservoir (ΔS_reservoir) is positive because heat is transferred from the reservoir to the water. On the other hand, the entropy change of the water (ΔS_water) is negative because heat is transferred to the water.

When we sum up the entropy changes of the reservoir and the water, we get:

ΔS_universe = ΔS_reservoir + ΔS_water = Q_reservoir / T_reservoir + Q_water / T_water

Since the temperature of the reservoir is higher than the temperature of the water (T_reservoir > T_water), the heat transfer terms in the equation have opposite signs. This means that the positive entropy change of the reservoir dominates, and the overall entropy change of the universe (ΔS_universe) is positive.

Hence, the correct answer is option 'D' - the entropy change of the universe is always positive.